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最喜欢的颜色

Favorite Color

专题
Brainteaser / 脑筋急转弯
难度
L2

题目详情

在一群人中，每个人最喜欢的颜色要么是红色、蓝色、黄色，要么是绿色。如果有 15 个人最喜欢的颜色不是红色，23 个人最喜欢的颜色不是蓝色，20 个人最喜欢的颜色不是黄色，17 个人最喜欢的颜色不是绿色，那么总共有多少人？

In a group of people, each person's favorite color is either red, blue, yellow, or green. If 15 people's favorite color isn't red, 23 people's favorite color isn't blue, 20 people's favorite color isn't yellow, and 17 people's favorite color isn't green, how many total people are there?

解析

对每种颜色而言，最喜欢该颜色的人数都等于总人数减去“不喜欢该颜色”的人数。因此：

  • 最喜欢红色的人数为 N−15N-15
  • 最喜欢蓝色的人数为 N−23N-23
  • 最喜欢黄色的人数为 N−20N-20
  • 最喜欢绿色的人数为 N−17N-17

因为每个人都恰好有一种最喜欢的颜色，所以这些人数之和必须等于总人数 NN：

N=(N−15)+(N−23)+(N−20)+(N−17)N = (N-15) + (N-23) + (N-20) + (N-17) \\

于是有：

N=4N−(15+23+20+17)N=4N−75N=25N = 4N - (15 + 23 + 20 + 17) \\ N = 4N - 75 \\ \boxed{N = 25}

Original Explanation

For each color, the number of people who favor that color is the total number of people minus the number of people whose favorite color is not that color. Therefore:

  • The number of people who favor red is N−15N-15
  • The number of people who favor blue is N−23N-23
  • The number of people who favor yellow is N−20N-20
  • The number of people who favor green is N−17N-17

Since everyone in the group has a favorite color, the sum of these numbers must equal the total number of people, NN:

N=(N−15)+(N−23)+(N−20)+(N−17)N = (N-15) + (N-23) + (N-20) + (N-17) \\

This means that:

N=4N−(15+23+20+17)N=4N−75N=25N = 4N - (15 + 23 + 20 + 17) \\ N = 4N - 75 \\ \boxed{N = 25}